Mega-Mart, a discount store chain, is to build a new store in Rock Springs. The parcel of land the company has purchased is large enough to accommodate a store with 140,000 square feet of floor space. Based on marketing and demographic surveys of the area and historical data from its other stores, Mega-Mart estimates its annual profit per square foot for each of the store’s departments to be as shown in the table on the following page. Each department must have at least 15,000 square feet of floor space, and no department can have more than 20% of the total retail floor space. Men’s, women’s, and children’s clothing plus housewares keep all their stock on the retail floor; however, toys, electronics, and auto supplies keep some items (such as bicycles, televisions, and tires) in inventory. Thus, 10% of the total retail floor space devoted to these three departments must be set aside outside the retail area for stocking inventory. Mega-Mart wants to know the floor space that should be devoted to each department in order to maximize profit.
a. Formulate a linear programming model for this problem.
b. Solve this model by using the computer.
Department ..... Profit per ft.2
Men’s clothing ...... $4.25
Women’s clothing ..... 5.10
Children’s clothing ....... 4.50
Toys ............ 5.20
Housewares ......... 4.10
Electronics ........ 4.90
Auto supplies ....... 3.80